# A Guide to Trading Systems

## 14.1 - Understanding the Position Sizing

Although the discussion of pair trading was supposed to be finished with the previous chapter I felt I needed to talk about a unique case before we wrap up. This chapter will be kept short.

Here you are.

I went through the pair trading algorithm y'day night (28 th May), and discovered a very interesting trade. These are the regression parameters.

• Stock X = ICICI Bank
• Stock Y = HDFC Bank
• Beta = 0.79
• Intercept = 1626
• Std_err = 2.67

It's amazing! It's perfect, isn’t it? Its ICICI, HDFC, and HDFC are two of the biggest private sector banks. They have similar business models, have similar revenue streams, and both are regulated by RBI. This is the ideal candidate for a pair trade.

The Adf value of 0.048 means that there is only 4.8% chance the residual will be non-stationary. There is about 95.2% chance the residuals will be stationary. This is amazing.

The std_err value is +2.67. This is the perfect residual value for initiating a short pair trade. This trade is short HDFC, and long ICIC.

How do we position this size? These are the details about price and lot size.

• HDFC Fut Price = 224.8
• HDFC Lot Size = 500
• ICICI Fut Price = 298.8
• ICICI Lot Size = 2750

We have already discussed the topic of position size in chapter 1. We will examine the beta to estimate the required number of shares for this trade.

The beta is 0.79. This means that every 1 share of Y must be offset by 0.79 shares of the same X. 500 shares are needed to offset the beta.

Can you see the problem? There is no way that the lot sizes can match.

It is not possible to trade one lot here each like in the TATA Motors DVR example and Tata Motors DVR example. This will not be a beta neutral transaction if we do.

To position this correctly, we must work with lot sizes.

The lot size for ICIC is 2750. Beta is 0.79. HDFC's lot size is 500. Given that HDFC has a larger lot than ICICI, how many HDFC shares should there be to beta neutralize 2750 ICICI shares?

This is how we figure it out: Simply divide -

2750/0.79

= 3481.01

We can increase this to 3500, as the lot size for HDFC is 500. Given the 500-lot HDFC lot size, there will be 7 lots HDFC to 1 lot ICICI.

## 14.2 - Seize

Okay, now that we have the position size, the big question is: will you trade this?

Everything looks perfect. ADF has a desirable price, residual is at 2.67 SD. The two stocks are closely related, and the business is very similar. What could go wrong?

Yes, it looks great. But if we consider the closer inspection, it depicts a different scenario.

This is why we must quickly review the regression equation.

= Beta *x + Intercept + Residual

This equation is a way to think about how we can explain the stock market price of Y by multiplying the stock price X by its beta. The intercept is basically the portion of y's stock market price that the model can't explain. The residual is the difference between actual and predicted y.

This means that the regression model cannot explain a large proportion of Y's stock prices.

The intercept in this instance is 1626. HDFC's stock price is 2024 per share. This means that the regression equation cannot explain 1626 of 2024. The regression equation cannot explain almost 80% (1626/2024), of Y's stock market price. In other words, it can only explain 20% of the equation. This is very tricky.

This implies that we are trading very little probability when we trade this pair. This is something I would prefer to avoid and find another way to trade. Although I do know traders who would love this trade, for me, the risk is more important than the reward.

Best of luck!